I am going to do favorite episodes instead of scenes or moments because that is a bit overwhelming. I have a lot of favorite scenes.
I am going to have to sort this by Doctor. I have episodes that are favorites for certain Doctors.
Ninth Doctor: The Empty Child: As creepy as this episode is. I really really liked the ending. Anything that has to do with a mother and her children has always had a deep meaning for me. I can't explain it. Dumbo makes me cry every single time I watch it.
I don't have very many favorite episodes with the Ninth Doctor. It is not that I don't like his Doctor. I really like Christopher Ecleston as an actor and I like his doctor. His episodes just have not made as much of an impression on me.
Tenth Doctor: The Shakespeare Code: I love Shakespeare so how could I not get excited about this episode. Not to mention all the Harry Potter references! I have always had a strong notion of the power of words and this episode explored how words can be powerful.
The Girl In The Fireplace: My whole family loved this episode because when we watched it we had just heard our priest speak about how God experiences all of time at once and this helped us see how that could be. God was like the Doctor and we were like Reinette.
Silence In The Library & Forest of the Dead: I am not entirely sure why I like these two so much. I think it has to do with River. I love River she is totally awesome but she also scares me sometimes. Also it has a library that was so huge it had it's own planet. There is also the idea that books can be so real that they can be another world to us.
Eleventh Doctor: The Time of Angles & Flesh and Stone: Again River. We get to learn more about her but also have more questions. Getting to know Matt Smith's Doctor was another reason I liked this episode.
The Doctor's Wife: This episode has to be my most favorite from Eleven. I just love the Tardis and the Doctor getting to talk and well. It is just amazing. :) I just loved watching how the Tardis had to learn to cope with the real world outside of her Box. The Doctor always has his box even it his box is not in it's box.
Let's Kill Hitler: River again. I really just enjoyed this episode. Honestly who doesn't want to go back in time and put Hitler in a cupboard?
There are many many other episodes that I like. These are just the ones that I thought of first.